An efficient optimization of measurement matrix for compressive sensing

Compressive sensing (CS) is a new paradigm for signal acquisition and reconstruction, which can reconstruct the signal at less than the Nyquist sampling rate. The sampling of the signal occurs through a measurement matrix (MM); thus, MM generation is significant in the context of the CS framework. In this paper, an optimization algorithm is introduced for the generation of the MM of CS based on Restricted Isometric Property (RIP) mandates that eigenvalues of the sensing matrix fall within an interval also minimizes the mutual coherence of the sensing matrix (i.e. the product of the MM and sparsifying matrix). A novel gradient-based iterative optimization method is used to reduce the eigenvalues of the sensing matrix by SVD decomposition. Meanwhile, the proposed algorithm can also reduce the operational complexity. Experimental results and analysis prove that the optimized MM reduces the maximum mutual and average mutual coherence between the MM and the sparsifying basis, which shows the effectiveness of the proposed algorithm over some state-of-art works.